3(x+6)3x=14

Solution for 3(x+6)3x=14 equation:

Simplifying
3(x + 6) * 3x = 14

Reorder the terms:
3(6 + x) * 3x = 14

Reorder the terms for easier multiplication:
3 * 3x(6 + x) = 14

Multiply 3 * 3
9x(6 + x) = 14
(6 * 9x + x * 9x) = 14
(54x + 9x2) = 14

Solving
54x + 9x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 54x + 9x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 54x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.555555556 + 6x + x2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + 6x + 1.555555556 + x2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + 6x + x2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + 6x + x2 = 0 + 1.555555556
6x + x2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
6x + x2 = 1.555555556

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1.555555556 + 9

Reorder the terms:
9 + 6x + x2 = 1.555555556 + 9

Combine like terms: 1.555555556 + 9 = 10.555555556
9 + 6x + x2 = 10.555555556

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10.555555556

Calculate the square root of the right side: 3.248931448

Break this problem into two subproblems by setting 
(x + 3) equal to 3.248931448 and -3.248931448.

Subproblem 1
x + 3 = 3.248931448

Simplifying
x + 3 = 3.248931448

Reorder the terms:
3 + x = 3.248931448

Solving
3 + x = 3.248931448

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 3.248931448 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.248931448 + -3
x = 3.248931448 + -3

Combine like terms: 3.248931448 + -3 = 0.248931448
x = 0.248931448

Simplifying
x = 0.248931448

Subproblem 2
x + 3 = -3.248931448

Simplifying
x + 3 = -3.248931448

Reorder the terms:
3 + x = -3.248931448

Solving
3 + x = -3.248931448

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = -3.248931448 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.248931448 + -3
x = -3.248931448 + -3

Combine like terms: -3.248931448 + -3 = -6.248931448
x = -6.248931448

Simplifying
x = -6.248931448

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.248931448, -6.248931448}